QFT: Questions About Vector Field, Polarization Vectors & Space

[alanzhu]

Hello everyone, I am now learning QFT, this theory is really abstract and daunting. I can't understand the concept of vector field. What is vector field at last? why there are four polarization vectors? I feel that the whole theory is somewhat lack of reasoning, the postulates and assumptions really confuse me. Could someone explain why there are 3 kinds of space and what is the most distinct difference between them.

 

[selfAdjoint]

Could you explain what three kinds of space, please?

A vector field is a phenomenon that is characterised by a magnitude and a direction at each point of space - for example the gravity field near the Earth has an acceleration (a vector with magnitude and direction) at every point, and different values at different points. No?

 

[gnl]

I suspect it also necessary for you to realize that there is a lot of classical field theory in QFT. Vector fields are a perfectly classical notion. Electric and magnetic fields are examples. In relativistic field theories, you get 4-vectors (this tells you how they transform under Lorentz transformations). I suggest you start by reviewing classical mechanics (Goldstein), then move to classical fields (Jackson on electrodynamics); then, only then, pass to something like Peskin and Schroeder or Bjorken and Drell (QFT).

 

[selfAdjoint]

...and before those QFT texts, you also need to study a nonrelativistic QM book. Sakurai is the classic one.

 

[gnl]

I could not agree more! Sakurai is a text all physicists should read. The best on QM.

 

[Imparcticle]

What is QFT an acronym for? Quantum...?

 

[gnl]

Qft

Quantum Field Theory. The quantised theory of fields.